computing_corrected_estimator

This function computes the corrected estimator for a linear model
with measurement error in covariates by solving the corrected
estimating equations using a nonlinear root-finding algorithm.

internal

Estimation and inference for coefficients of linear EIV models with symmetric measurement errors.
The measurement errors can be homoscedastic or heteroscedastic, for the latter, replication for at least some observations needs to be available. The estimation method and asymptotic inference are
based on a generalised method of moments framework, where the estimating equations are formed from (1) minimising the distance between the empirical phase function (normalised characteristic function) of the response and that of the linear combination of all the covariates at the estimates,
and (2) minimising a corrected least-square discrepancy function. Specifically, for a linear EIV model with p error-prone and q error-free covariates, if replicates are available, the GMM approach is based on a 2(p+q) estimating equations if some replicates are available and based on p+2q estimating equations if no replicate is available.
The details of the method are described in Nghiem and Potgieter (2020) <doi:10.1093/biomet/asaa025> and Nghiem and Potgieter (2025) <doi:10.5705/ss.202022.0331>.

Chang Liu

PhaseGMM

Phase-Function Based Estimation and Inference for Linear
Errors-in-Variables (EIV) Models

Linh Nghiem

computing_corrected_estimator function

<dl><dt>y</dt>
<dd>Numeric vector of length <code>n</code>. Response variable.</dd>
<dt>Wbar</dt>
<dd>Numeric matrix of dimension <code>n × p</code>. Error-prone
covariates at the averaged (replicate) level.</dd>
<dt>Zmat</dt>
<dd>Numeric matrix of dimension <code>n × q</code>. Error-free
covariates (including intercept if applicable).</dd>
<dt>estSigmaU_bar</dt>
<dd>Measurement error variance/covariance associated
with the averaged covariates. Can be <code>n × p × p</code> or <code>n × 1</code>.</dd>
<dt>beta_in</dt>
<dd>Optional numeric vector of length <code>p + q</code>. Initial
value for the estimating equation solver.</dd></dl>

Arguments

Compute the corrected estimator via estimating equations — computing_corrected_estimator

<dl>

<dt>y</dt>
<dd>Numeric vector of length <code>n</code>. Response variable.</dd>


<dt>Wbar</dt>
<dd>Numeric matrix of dimension <code>n × p</code>. Error-prone
covariates at the averaged (replicate) level.</dd>


<dt>Zmat</dt>
<dd>Numeric matrix of dimension <code>n × q</code>. Error-free
covariates (including intercept if applicable).</dd>


<dt>estSigmaU_bar</dt>
<dd>Measurement error variance/covariance associated
with the averaged covariates. Can be <code>n × p × p</code> or <code>n × 1</code>.</dd>


<dt>beta_in</dt>
<dd>Optional numeric vector of length <code>p + q</code>. Initial
value for the estimating equation solver.</dd>

</dl>

computing_corrected_estimator: Compute the corrected estimator via estimating equations

Description

Usage

Value

Arguments

Details

See Also